61 citations · 100 across the 13 of their papers we have counts for
16 papers
The dual of the Tits cone and dominance of Coxeter groups
Xiang Fu, Jiaqing Gu, Mengfan Lyu +3
In this paper we introduce a potentially infinite process of reflections applied to a sequence of points in the dual of the Tits cone associated with an arbitrary finitely generate…
A deformation theorem for Poincaré duality pairs in dimension 3
Lawrence Reeves, Peter Scott, Gadde A. Swarup
We prove the analogue of Johannson's Deformation Theorem for PD3 pairs.
Irrational-slope versions of Thompson's groups and
José Burillo, Brita Nucinkis, Lawrence Reeves
In this paper we consider the - and - versions, and , of the irrational slope Thompson group considered in [3]. We give infinite presentations for these gro…
Comparing decompositions of Poincaré duality pairs
Lawrence Reeves, Peter Scott, Gadde Swarup
Analogues of JSJ decompositions were developed for Poincaré duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splitting…
Affine reflection subgroups of Coxeter groups
Xiang Fu, Lawrence Reeves, Linxiao Xu
In this paper we study affine reflection subgroups in arbitrary infinite Coxeter groups of finite rank. In particular, we study the distribution of roots of Coxeter groups in the r…
Neighbourhoods in root systems of infinite Coxeter groups
Yuhan Cai, Xiang Fu, Lawrence Reeves
Let be a finitely generated infinite Coxeter group, with and being the corresponding root system and set of simple roots respectively. It has been observed by Hohlweg e…
An Irrational-slope Thompson's Group
José Burillo, Brita Nucinkis, Lawrence Reeves
The purpose of this paper is to study the properties of the irrational-slope Thompson's group introduced by Cleary in 1995. We construct presentations, both finite and infini…
Mapping the Davis complex into the imaginary cone
Xiang Fu, Lawrence Reeves
The study of the set of limit roots associated to an infinite Coxeter group was initiated by Hohlweg, Labbé and Ripoll and further developed by Dyer, Hohlweg, Péaux and Ripoll. The…
Commutators in groups of piecewise projective homeomorphisms
José Burillo, Yash Lodha, Lawrence Reeves
In 2012 Monod introduced examples of groups of piecewise projective homeomorphisms which are not amenable and which do not contain free subgroups, and later Lodha and Moore introdu…
Some non-contracting automata groups
Nick Davis, Murray Elder, Lawrence Reeves
We add to the classification of groups generated by 3-state automata over a 2 letter alphabet given by Bondarenko et al., by showing that a number of the groups in the classificati…
On the genus of infinite groups
Iain Aitchison, Lawrence Reeves
We associate to each finite presentation of a group G a compact CW-complex that is a 3-manifold in the complement of a point, and whose fundamental group is isomorphic to G. We use…
On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
Martin R. Bridson, Lawrence Reeves
We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to th…
A Combination Theorem for Strong Relative Hyperbolicity
Mahan Mj, Lawrence Reeves
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension o…
Groups acting on CAT(0) cube complexes
Graham A. Niblo, Lawrence Reeves
We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian m…
Central Extensions of Word Hyperbolic Groups
Walter Neumann, Lawrence Reeves
Thurston has claimed (unpublished) that central extensions of word hyperbolic groups by finitely generated abelian groups are automatic. We show that they are in fact biautomatic.…
Regular Cocycles and Biautomatic Structures
Walter D. Neumann, Lawrence Reeves
Let be a virtually central extension of the group by a finitely generated abelian group . We show that carries a biautomatic structure if and only if has a biaut…